Can RNNs get inputs and produce outputs similar to the inputs and outputs of FFNNs?
Yes, it is possible. What you have shown in case of ANN is what happens in a regression model using NNs. What you have shown in case of RNN is what happens when you are doing sequence-to-sequence translation (like French to English).
If you want to get single values like in case of ANN, suppose you are doing regression, then, in the end, you will flatten the features aggregated by RNN (in case of Tensorflow, use Flatten layer and in case of PyTorch, you can directly do it). It should be then followed by a dense layer of 3 (in case of Tensorflow) or linear layer of 3 (in case of PyTorch), if I am talking about your example.
Since, you have shown values above 1, I presume you are doing some kind of regression. But, it would be good idea to normalize your outputs in case of regression, it makes the optimization easier.
If you want to classification then in the last layer, use Dense layer with softmax (in case of Tensorflow) and softmax followed by a linear layer (in case of PyTorch).